Well, answering as a Catholic I am bound by dogma. However this piece
here is worth a read and goes into some detail as to why the Church isn't sexist.
That article does not in any way answer the question as to why women cannot be priests. You have not stated why women cannot be priests. At no point have you been able to answer the question as to what makes a women unable to perform the duties of a priest.
But really the Church position is clear.
Women are unable to be priests.
Which is sexist. Because there is no solid reasoning for why women are unable to be priests especially when looking at so many other religions were they do quite admirably in the same role.
It doesn't teach that it doesn't want female priests - it simply teaches that they are not capable of being priests.
As a man I am not capable of bearing children - does that mean I am not equal to a woman?
The difference being I can give you a very solid reason as to why you are incapable of bearing children (you lack a womb and the other necessary plumbing) whilst you have so far been unable to do so for the question of why women are incapable of being priests.
I am not stopping you from living your life in any way that you so choose. It doesn't mean that contraception has a bearing on sexual equality. Your wife on the other hand as a Catholic should try to adhere to the teaching of the Church.
Worry not, she no longer uses contraception. Unless having sex with a man who has had a vasectomy is a sin? In which case, she sins on a regular basis.

Whilst you may not be trying to stop me from living my life in any way that I choose your church most certainly is trying to stop others from living their lives in ways they choose.
I believe that, and I believe that people sin. I am not perfect by any stretch. I personally don't have too much of an issue with gay civil partnerships, I have a very strong objection to gay marriage.
So you honestly believe that the fact gay men (and women obviously) have the right to marry someone of the opposite gender makes the Catholic churches objections to gay marriage acceptable? Would the right to worship be OK if it only allowed Anglican Worship?
I believe that "the lobby" was pretty clear at the time. Certainly the Catholic Church believes that gay partnerships erode the value placed on the family.
Yeah, with absolutely no evidence for it.
The Catholic Church believes homosexual acts are wrong. Do you really expect them to endorse the adoption of a child by parents who are doing wrong? Really? You might not agree with them but at least understand them. They really can't take any other position.
Haven't you yourself said that all people sin? Surely then the Catholic Church will always be placing a child with parents that are doing wrong? Are you aware of what our care system is like (without going in to what the Catholic run care system in Ireland was like..)? Considerably more damage is likely to be done leaving a child in care than haivng them adopted by a gay couple.
I am not judging just stating fact. I am sure your wife is lovely and I am most certainly not judging her - that isn't my place.
How on earth is calling her a heretic not judging her? (Though to be fair, you alluded to any person believing that to be a heretic and I was the one that mentioned my wife...)
I am aware that there are members of the Catholic Church who would like to see women ordained. Those people are either (a) ignorant of their own religion or (b) heretics.
Or (c) Able to think critically for themselves and realise that sometimes the Catholic Church is not always doing things guided by god. Unless you think the selling of indulgences was also OK?
The Churches position is that women can not be priests - that is an infallible dogma. It can not be changed.
It changed it's mind on the status of married clergy at least once so far (and sort of a second time too). Seems that these things can be changed after all.
If your wife is aware of this and still rejects it then she is committing the sin of heresy. This is a very grave sin indeed and carries the sanction of excommunication. I don't want to sound too dramatic on this but essentially the Church has rules and if you want to stay in the Church you have to follow the rules. She is not bound to the Church and can follow the path to apostasy if she chooses.
I shall let her know, she can have a word with the priest and see what the process is. It is going to play havoc with school places though and the mother in law will probably blame me which will make Christmas Dinner akward.
Alternatively it could quite possibly be that questioning the chruch isn't grounds for excommunication any more? As long as my wife doesn't actually go and get ordained she hasn't really commited the sin of heresy.